Nonparametric Methods in Continuous-Time Finance: A Selective Review

This paper gives a selective review on the recent development of nonparametric methods in continuous-time finance, particularly in the areas of nonparametric estimation of diffusion processes, nonparametric testing of parametric diffusion models, and nonparametric pricing of derivatives. In each financial context, we discuss suitable statistical concepts, models, procedures, as well as some of their applications to financial data. Much theoretical and empirical research is needed in this area, and we point out several aspects that deserve further investigation.